On Doubly Transitive Groups of Degree n and Order 2(n − 1)n

Abstract

Let 5 denote the icosahedral group and let be the normalizer of a Sylow 5-subgroup of 5. Then the index of in 5 equals six. Let us represent 5 as a permutation group A on the set of residue classes of with respect to 5 Then it is clear that A is doubly transitive of degree 6 and order 60 = 2·5·6. Since 5 is simple, A does not contain a regular normal subgroup.